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Let `f,g: RvecR` be two functions defined as `f(x)=|x|+x` and `g(x)=|x|-x` , for all `xRdot` Then find fog and gof.

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Given,
`f(x)=|x|+x` and `g(x)=|x|−x `
`∴fog=f(g(x)) `
`=>fog=f(|x|−x) `
`=>fog=||x|−x|+|x|−x`
Now,
...
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RD SHARMA-FUNCTION-Solved Examples And Exercises
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  3. Let f,g: RvecR be two functions defined as f(x)=|x|+x and g(x)=|x|-x ,...

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  6. Find fog(2) and gof(1) when: f: R rarr R ;f(x)=x^2+8 and g: R rarr ...

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  7. Find gof and fog when f: R->R and g: R->R is defined by f(x)=x and g(x...

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  12. Let A={a ,\ b ,\ c} , B={u\ v ,\ w} and let f and g be two functions f...

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  13. Find fog\ (2) and gof\ (1) when: f: R->R ; f(x)=x^2+8 and g: R->R ; g(...

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  14. Let R^+ be the set of all non-negative real numbers. If f: R^+\ ->R...

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  15. Let f: R->R and g: R->R be defined by f(x)=x^2 and g(x)=x+1 . Show tha...

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